Preparation

Purée tomatoes, cucumbers, celery, and horseradish in a blender until smooth. Strain through a cheesecloth-lined fine-mesh sieve into a large bowl. Let drain, without stirring, until 3 cups of liquid are collected, about 2 hours; discard solids in strainer. Season to taste with salt, pepper, and sugar.

Divide tomato water among 6 ice-filled glasses. Top each glass with 2 Tbsp. (or more) vodka. Garnish with lemon slices and cucumber spears.